A honeycomb lattice model simulating the surface states of topological insulators

A honeycomb lattice model exhibiting the quantum spin-Hall effect is proposed, where the low-energy properties of the electrons are mainly determined by the energy spectrum in the vicinity of the Γ point, for suitable parameters. The nontrivial topology of the energy bands is revealed by calculating the Chern numbers, Berry curvature distribution, and edge state spectrum. We further show that in the continuum limit, the model Hamiltonian is equivalent to the effective model for the surface states in thin films of three-dimensional topological insulators. As a consequence, this lattice model provides a useful tool for numerical simulation of the physical properties of the surface states.